u/Simpson17866

The general form of these series is that each term is a power of 10 (since moving the decimal takes no effort) multiplied or divided by a single-digit number (since single-digit multiplication/division takes far less effort than multi-digit multiplication/division).

It follows the basic principle of simple repeated fractions, but with only adding and subtracting error terms (no taking reciprocals and then cross-multiplying) and with having multiple options at each step from which to choose the best (rather than being given one automatically).

Taking π = 3.14159265, for example, we would start with either 3 (underestimating with 10^n times x), 4 (overestimating with 10^n times x), 10/4 (underestimating with 10^n divided by x), or 10/3 (overestimating with 10^n divided by x).

3 is the closest starting point (error of 0.14159265) and 3.33333333 is almost as close (error of 0.19170408), so we would throw 4 and 2.5 away and test 3 first, then 3.33333333.

The error “π – 3 = 0.14159265…” can be estimated as 1/10, as 2/10 (which could be re-written as 1/5, but that doesn’t matter here because we’re about to ignore it anyway), as 1/8, or as 1/7.

1/7 and 1/8 are the closest second-steps for π ≈ 3, so we throw away the 1/10 and the 2/10, and now we see what the closest second-steps would be for π ≈ 10/3.

The error “π – 3.33333333 = -0.1917408” would best be approximated as -0.2 (which could be written as -1/5 or -2/10 depending on the reader’s personal preference), but the two-step calculations 10/3 – 1/5 = 3.1333333333 and 3 + 1/8 = 3.125 are both less accurate than the two-step calculation 3 + 1/7 = 3.14285714, so we can commit to 3 + 1/7 now.

Calculating the new error “π – (3 + 1/7) = -0.00126449” creates a best new error term of -1/800, and so our new value is 3 + 1/7 – 1/800 = 3.14160714.

This approximation “πx ≈ 3x + x/7 – x/800” is accurate to within 1 part in 220,000, but it only takes about as much time and effort as “πx ≈ 3x + x/10 + 4x/100” (which is only accurate to within 1 part in 2,000).

Using continued fractions would take very little time to calculate “π ≈ 355/113” ahead of time (which is accurate to within 1 part in 12,000,000), but this takes more time and effort to use in the moment. If someone was multiplying πx ≈ 3x + x/7 – x/800 and if someone else was multiplying πx ≈ (300x + 50x + 5x)/113, then in the time it took the first person to get a final answer, the second person would only have finished calculating the numerator, and they would still need time to calculate the denominator.

During which time, the first person could be adding more error terms: 3 + 1/7 – 1/800 – 1/70,000 is accurate to within 1 part in 15,000,000 (already more accurate than 355/113 for less time and effort), and 3 + 1/7 – 1/800 – 1/70,000 – 1/5,000,000 is accurate to within 1 part in 880,000,000.

The general form of these series is that each term is a power of 10 (since moving the decimal takes no effort) multiplied or divided by a single-digit number (since single-digit multiplication/division takes far less effort than multi-digit multiplication/division).

It follows the basic principle of simple repeated fractions, but with only adding and subtracting error terms (no taking reciprocals and then cross-multiplying) and with having multiple options at each step from which to choose the best (rather than being given one automatically).

Taking π = 3.14159265, for example, we would start with either

• 3 (underestimating with 10^n times x)

• 4 (overestimating with 10^n times x)

• 10/4 (underestimating with 10^n divided by x)

• or 10/3 (overestimating with 10^n divided by x).

3 is the closest starting point (error of 0.14159265) and 3.33333333 is almost as close (error of 0.19170408), so we would throw 4 and 2.5 away and test 3 first, then 3.33333333.

The error “π – 3 = 0.14159265…” can be estimated as

• 1/10

• 2/10 (which could be re-written as 1/5, but that doesn’t matter here because we’re about to ignore it anyway)

• 1/8

• or 1/7.

1/7 and 1/8 are the closest second-steps for π ≈ 3, so we throw away the 1/10 and the 2/10, and now we see what the closest second-steps would be for π ≈ 10/3.

The error “π – 3.33333333 = -0.1917408” would best be approximated as -0.2 (which could be written as -1/5 or -2/10 depending on the reader’s personal preference), but the two-step calculations 10/3 – 1/5 = 3.1333333333 and 3 + 1/8 = 3.125 are both less accurate than the two-step calculation 3 + 1/7 = 3.14285714, so we can commit to 3 + 1/7 now.

Calculating the new error “π – (3 + 1/7) = -0.00126449” creates a best new error term of -1/800, and so our new value is 3 + 1/7 – 1/800 = 3.14160714.

This approximation “πx ≈ 3x + x/7 – x/800” is accurate to within 1 part in 220,000, but it only takes about as much time and effort as “πx ≈ 3x + x/10 + 4x/100” (which is only accurate to within 1 part in 2,000).

Using continued fractions would take very little time to calculate “π ≈ 355/113” ahead of time (which is accurate to within 1 part in 12,000,000), but this takes more time and effort to use in the moment. If someone was multiplying πx ≈ 3x + x/7 – x/800 and if someone else was multiplying πx ≈ (300x + 50x + 5x)/113, then in the time it took the first person to get a final answer, the second person would only have finished calculating the numerator, and they would still need time to calculate the denominator.

During which time, the first person could be adding more error terms: 3 + 1/7 – 1/800 – 1/70,000 is accurate to within 1 part in 15,000,000 (already more accurate than 355/113 for less time and effort), and 3 + 1/7 – 1/800 – 1/70,000 – 1/5,000,000 is accurate to within 1 part in 880,000,000.

When I watched 2018’s She-Ra and the Princesses of Power, I fell in love with the plot and character arcs, but the worldbuilding of the planet of Etheria was notoriously shallow (with each “kingdom” being 10 people and being a day’s walk from all the other kingdoms), so when I started writing a fanfiction about one of the most popular plot divergences in the fandom, my furthest-reaching goal was to flesh out the worldbuilding so that the world would have actual civilizations and so that the war would have actual battles with strategy, tactics, and logistics.

My basic starting point was to slightly tone down the “SciFi versus Fantasy” dichotomy from the original canon’s world:

• In canon, the Fantasy kingdoms operate at a roughly Medieval level (absolute monarchies with no firearms) and the SciFi empire’s army revolves primarily around gigantic spider-drones and hover-tanks.

• In my version, the Fantasy kingdoms start out closer to an Enlightenment equivalent (constitutional monarchies with limited firearms), and the SciFi empire hasn’t started producing giant robots yet (hovertanks still exist, but now the backbone of the army is soldiers with plasma blasters).

This was originally just supposed to be the backdrop of a military thriller, but over the last 5 years of outlining, the cultural and political backdrops have also become much more important than they were originally supposed to be.

• Most of the kingdoms fighting against the Horde are in various stages of transitioning from feudalism to capitalism, with the primary kingdom of Bright Moon being the most moderate of the big three.

• When most of the fandom’s left-leaning fanfic authors flesh out The Horde with an actual political philosophy beyond “evil army taking over the world,” they tend to portray the Horde as fascists, but I decided early on that I wanted to see what would be different if I made them more Marxist-Leninist instead.

• In canon, we’re told that the Hippy Pacifist™ kingdom of Plumeria had maintained pacifist cultural traditions for “thousands of years.” I’m re-imagining Plumeria as a loose confederation of anarchist communes, and I’ve decided that their anarcho-pacifist culture is a recent development — 60 years ago, a civil War between Plumerian noble houses got so bad that both armies refused to fight each other anymore and forcibly dissolved the monarchy instead.

This project started while I was taking a World War One history class — I learned a lot about how the Industrial Revolution changed the face of warfare, and as a lifelong D&D nerd, I immediately started asking myself "if a D&D world's Industrial Revolution was based on magical 1400s technology instead of on non-magical 1800s technology, how would the WWI equivalent have been different?"

The most important principles that I originally started with were

• The minotaurs started out the least technologically advanced, but the most industrially efficient with the limited technology they did have. One of the more advanced nations tried to rebuild minotaur society in their own image by teaching the most advanced minotaur archmages their own most advanced knowledge in exchange for recruiting them as local colonial governors — instead, the minotaur archmages kicked off an Industrial Revolution by combining their patrons' superior technological knowledge with their own superior industrial philosophy, and the rest of the world's empires found themselves scrambling to catch up from the opposite direction (combining their own superior technology with the minotaurs' superior industrial philosophy)

• The humans and the orcs have settled their differences and formed a multi-ethnic superpower together, and the Great War itself revolved around the humans and the orcs on one side versus the goblins (small and yellow-green), the hobgoblins (human-sized and orange-red), and the bugbears (tall, brown-black, extremely furry) on the other

• The war eventually got so bad that both armies mutinied against their commanders together and refused to fight anymore.

I was originally throwing the D&D Kitchen Sink together (humans, orcs, elves, dwarves, goblins, hobgoblins, bugbears, lizardfolk, kobolds, dragonborn, tabaxi (catfolk)), but I decided to cut the dwarves, the elves, the kobolds and the dragonborn, and I brought the lizardfolk and the catfolk together into a single faction.

My new backstory is that there's some other continent off-screen that plays by more traditional dynamics (humans, elves, and dwarves being united against orcs), but that the first explorers from The Old Country to land on the main continent (populated by goblins and minotaurs in the north and lizardfolk and catfolk in the south) were humans and orcs.

These settlers originally brought their ancestral wars with them, but after a couple of generations, they decided they liked each other better than their overlords in The Old Country, so they joined forces and formed their own new nations together (forming alliances with the lizardfolk/catfolk against the goblins).

(In my original version, the minotaurs learned their new technology from the elves, but in my new version, they learned it from the goblins).

Worgs have also become more important :) In typical D&D settings, worgs are gigantic, demonic wolves that range from "domesticated beasts owned by goblins" to "sapient people who are technically enslaved by goblins and used as beasts, but are too bloodthirsty to care as long as their masters let them kill people."

In my Industrial setting, worgs more closely resemble gigantic hyenas (shorter tails and snouts), and their relationship with goblins is overwhelmingly that of an equal partnership — worgs are bigger, stronger, and faster, but goblins have opposable thumbs for making and using tools, and a worg mount and a goblin rider tend to be more personally close with each other than they are with their mates of their own species.

The cultural founding myth even says that it was two worgs who first proposed partnerships with goblins.

For a couple of weeks now, I’ve noticed that a lot of the most interesting prompts that users have posted for have gotten removed within a day or two because the Original Post itself wasn’t specifically a piece of the Original Poster’s own worldbuilding.

But this seems counterproductive because the point of prompts is that other users reply with specific pieces of their own worldbuilding to the table that they might not have made an entire post about.

Or, if they had, then nobody would have talked with them about it because their OP would’ve been buried under other OPs that other users had to post, rather than everything being in one place as replies to a single OP.

The article starts with

> Authoritarian capitalism, or illiberal capitalism, is an economic system in which a liberal capitalist market economy exists alongside an authoritarian government. It overlaps significantly with state capitalism, a system in which the state undertakes commercial activities. However, it is distinct in its combination of private property and the functioning of market forces with restrictions on dissent, a complete lack of freedom of speech or significant limits on it, and either an electoral system with a single dominant political party or a lack of elections.

and then lists specific examples such as

> China since the reform and opening up; Russia, under Vladimir Putin; Chile, under Augusto Pinochet; Indonesia, under Suharto; Peru under Alberto Fujimori and Singapore, under Lee Kuan Yew. Additionally, the term is often applied to military dictatorships that received support from the United States during the Cold War era.

However, supporters of capitalism on this sub tend to refer to these dictatorships as "Not True Capitalism," arguing that capitalism is categorically defined by "low government" and that high government is categorically defined as "socialism."

If they're right, then should Wikipedia's article be removed for being politically incorrect?

This year, one capitalist charged his combined customer base a total of $6 billion for his workers to provide a good/service, and he paid his combined workforce a total of $1 billion, pocketing $5 billion profit.

The same year, another capitalist charged his combined customer base a total of $5 billion for his workers to provide the same good/service, and he paid his combined workforce a total of $2 billion, pocketing $3 profit.

The next year, in a truly free market where customers and workers aren’t obstructed from taking their business elsewhere, the first capitalist’s customers will buy the good/service from the second capitalist instead (who offers lower prices for the same good/service), and the first capitalist’s workers will work for the second capitalist instead (who offers higher wages for the same work).

The only way for the first capitalist to stay in business next year is to raise wages and lower prices (perhaps charging his customers $4 billion and paying his workers $3 billion, only pocketing $1 billion profit).

Without government intervention to prop up capitalist profits, competition in a truly free market will automatically reduce the share of the wealth that gets siphoned off by the capitalists and increase the share of the wealth that stays with the workers and the customers (drifting further and further away from capitalism and closer and closer to socialism).

When socialists argue in political forums “capitalism is abusive because workers are forced to do extra work for less benefit just so that their bosses can be the ones who get rich,”

Capitalism apologists insist “your boss doesn’t own your labor, YOU own your labor, and this means that the harder you work, the richer you get. This is good because rewarding you for working harder incentivizes you to work harder.”

And yet when real people talk about their real jobs in the real world, the most common description of life in a capitalist workforce is “There’s no reason to do more than the bare minimum — if I go above and beyond, my bosses get all the benefits, and I’m not sacrificing even more time out of my life for that.”

Where does this disconnect come from?

(I tried a post about this a year ago, but I was quickly told that I didn’t explain key characters’ motivations clearly, and I’ve also decided since then that I went into too much detail just making the math complicated.

I’d like to try again to keep the focus on the core principles.)

Say that a band is setting up a concert, and the largest venue available to them has 10,000 seats.

• If they charge $100 or less for tickets, then 10,000 fans will buy them (grossing $1 million or less)

• If they charge more for tickets, then not as many fans will buy them, and there will be a point where increasing the price eventually reduces their total revenue because “fewer tickets” outpaces “more money per ticket.”

• If they want to maximize sales, then the mathematically optimal market price is $200 each for tickets that 8,000 fans will buy, grossing $1.6 million

The band themselves are communists who would just as soon perform for free, but they live in a capitalist society where your legal access to the resources you depend on to stay alive (food, housing, medicine…) is calculated by how much money you have.

They have to balance their survival under capitalism on the one hand “we need to make as much money as possible from this job so that we can afford to keep doing it” with their human values on the other hand “we want as many of our fans to enjoy our concerts as possible as cheaply as possible,” so they decide to compromise by charging $100 per ticket with the intention of selling out all 10,000 seats.

But say that one billionaire does the same calculation and learns the same result (that sales are maximized when 8,000 fans buy tickets for $200 each), so he buys all 10,000 the tickets first and re-sells them for $200 each.

• 2,000 people will have to miss out on the concert because they can’t afford it anymore

• 8,000 will pay double what they originally needed to

• and the billionaire will collect $600,000 profit.

According to capitalist doctrine, people being rich is a sign that they worked hard to provide valuable goods/services that they offered to their customers in a voluntary exchange for mutual benefit.

What benefit did the fans of the band gain in exchange for the money that the billionaire collected from them?

I tried a post about this a few months ago, but in hindsight, I think I derailed my own point by putting too much initial focus on comparisons and contrasts against Karl Marx and Murray Rothbard.

Let me try again more directly:

• Do you think that Pierre-Joseph Proudhon was an anarchist or a socialist?

• Do you think that Mikhail Bakunin was an anarchist or a socialist?

• Do you think that Joseph Dejacque was an anarchist or a socialist?

• Do you think that Peter Kropotkin was an anarchist or a socialist?

• Do you think that Emma Goldman was an anarchist or a socialist?

• Do you think that Alexander Berkman was an anarchist or a socialist?

If you’re not an expert on every single one of these historical figures (and most of the people here probably aren’t), feel free to just focus on one or another ;)

Everyone here talks a lot about our absolute favorite socioeconomic systems, but I don’t see a lot of talk about what compromises people are most willing to make.

As a change of pace, if you were in the Ukrainian War Of Independence but knew that your own faction couldn’t win alone, who would you want to ally with (even if it meant your own faction lost anyway and all you did was put your partner faction in a stronger position to take over)?

As a refresher:

• Ukraine started out as a territory under the Russian Empire (feudal monarchy starting to experiment with capitalism)

• After the Russian monarchy was overthrown, they formed the Ukrainian People’s Republic (socialist democracy)

• which was overthrown by the Ukrainian State (capitalist dictatorship)

• The Russian Red Army (Bolshevik) and the Ukrainian Black Army (anarchist communist) joined forces against the Ukrainian State

• But then immediately went to war against each other

• Then formed a ceasefire when remnants of the monarchy’s White Army started to make a comeback

• And then the Bolsheviks slaughtered the anarchists, and Ukraine was swallowed up into the Soviet Union for the next 70 years.

(The Green Armies didn’t have a cohesive political ideology besides “fight the Red and White armies,” so I’m not including them)

I have abandoned and restarted a She-Ra longfic 4 times in the last 5 years — I have 68k words of notes outlined, but only 37k words of actual text.

I am going to bike to the library so that the effort of removing myself from my house reminds me to stay focused on actually writing :D

EDIT: Just wrote 700 words, and now I'm heading home :D

I'd forgotten how good the library is for writing, and I will bring my laptop charger next time so I can stay longer :)

I started writing it 5 years ago, but I only have 7 chapters written and nothing published, so I’m trying to motivate myself to write by telling myself “people are waiting for this” :)

I fell in love with She-Ra and the Princesses of Power for the plot and character arcs, but thought the world-building was extremely shallow, so I decided to write about what the popular fandom trope “Catra and Adora leave the Horde together” would look like in a version of the world with more fleshed-out worldbuilding.

Another fanfic author’s Reddit post mentioned reimagining the show’s “stereotypical hippy pacifist” kingdom of Plumeria as an anarchist commune, and I (a Social Democrat at the time) decided on a whim to do the same thing, so I started researching anarchist philosophy from the perspective of “This can’t realistically work in the real world, but what would it look like if it could work in a semi-unrealistic SciFi/Fantasy world?”

By the time I finished the first article I’d found, I was an anarchist, and a story that was supposed to be primarily a military thriller quickly became extremely political.

Some of the most important anarchist-specific worldbuilding points that I have so far are:

• The show (operating on Saturday Morning Cartoon logic) portrayed Plumeria’s pacifist culture as a tradition going back "thousands of years." In my more realistic worldbuilding, this is a much more recent development — 60 years ago, a civil war between Plumerian noble houses ended when both armies refused to fight each other and forcibly dissolved the monarchy instead.

• I was already planning on making the world bigger than canon’s “countries of 10 people who are all a day’s walk from each other,” so my version of Plumeria now being a loose confederation of communes means that different communes practice anarchism differently.

• In canon, the introduction to the Plumerians revolved around “the naïve pacifists need to be taught the importance of defending themselves.” I remember back when I wasn’t an anarchist, and an anarchist author taking canonically non-anarchist characters who make mistakes and turning them into anarchists who never make mistakes wouldn’t have convinced me to become one, so I need my anarchist Plumerians to make the same bad first impression that their canonical counterparts did — in my version, they’re being oppressed by a government official from a neighboring kingdom that they can’t defend against, and they need a more powerful official from the same government to intervene on their behalf (which most of my readers will initially misinterpret as an indictment against anarchism in general).

• Then, when the protagonists get to the most narratively-important Plumerian commune, my readers will be expecting me to flesh out the original “protagonists convince the pacifists to build an army” plot into “protagonists convince the anarcho-pacifists to rebuild a government and an army,” and my readers and protagonists will be caught off-guard together when the anarchists from the first commune offer a third option: “We need to figure out how to build anarchist militias so that we can defend each other on our own terms.”

• A historical irony is that my version of the Evil Horde is Marxist-Leninist-adjacent, rather than fascist, meaning that the anarchists and the monarchists are the ones who form awkward, dysfunctional alliances against the Marxist-Leninists

EDIT: I haven't done a lot of AMA posts before, and I forgot to add "Ask Me Anything" to the end of this one.

Ask Me Anything :D